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Activity 1 Direction: Write only the expressions or factorial notations in the 2nd column that will correspond to the solution of the following problems. The first one is done for you. Problems Expressions / factorial notations 1. How many quadrilaterals can be formed from 10 points such that 10C4 no three points are collinear? 2. How many 4-digit numbers that are divisible by 10 can be formed from the numbers 1, 3, 7, 8, 9, 0 such that repetitions of the number are not allowed? 3. In how many ways can 5 applicants for human resource officers, 4 jobseekers for I.T. programmers and 3 aspirants for graphic artists be seated in a row so that they are positioned alternatively? alternately? 4. In how many ways can 3 Bicolano books, 4 Cebuano books, and 2 llocano books be arranged on a shelf so that all books of the same dialects will be together? 5. In a department store, 10 jackets of different styles need to be displayed. In how many ways can the 10 jackets be hung on a circular rack? Activity 2 Modified True or False Direction: Write True if the mathematical solution in each problem is correct, otherwise write False if it is not. Put the correct solution in the given workspace and calculate the number of ways. The first one is done for you. Problems True/ Workspace False 1. How many polygons can be possibly formed from 5 distinct points on a plane, such that no three points are collinear? True 503 + 5C4 + 505 = 16 polygons 2. In how many ways can 8 graduating high school seniors' applicants for college admission and 3 panelists be seated at a 9! -(8! x 3!) ways round table if all the 3 panelists sit together? 3. How many different arrangements can be formed from the letters of the word, 10! / 2! ways PERMUTATION if each arrangement can be formed ends with letter "a" ? 4. A committee of 5 persons is to be formed from 6 men and 4 women. In how many ways can (402 x 6C3 ) + (4C1 x 6C4) this be done when at most 2 women are included? ways 5. In how many ways can 3 house keys, 2 car keys and 5 cabinet keys are to be arranged on 10! 31215! ways a key ring that has a clasp? Note: Clasp is a fitting device